Question

What is the length of the arc given that the radius is 12cm and the central angle is 4𝜋/3? Round your answer to the nearest tenth.

Answer 1

[AI-generated answer — Explain Bot]

To find the length of the arc, you can use the formula:

Arc Length = (Central Angle / 2𝜋) * Circumference

First, let's find the circumference of the circle using the formula:

Circumference = 2𝜋 * Radius

Given that the radius is 12 cm, we can substitute this value into the formula:

Circumference = 2𝜋 * 12
Circumference = 24𝜋

Now, we can substitute the values into the formula for arc length:

Arc Length = (4𝜋/3 / 2𝜋) * 24𝜋
Arc Length = (4𝜋/3) * (24𝜋 / 2𝜋)
Arc Length = (4𝜋/3) * 12
Arc Length = 16𝜋

To round the answer to the nearest tenth, we can substitute the value of 𝜋 with approximately 3.14:

Arc Length ≈ 16 * 3.14
Arc Length ≈ 50.24 cm

Therefore, the length of the arc is approximately 50.24 cm when rounded to the nearest tenth.